A339360 Sum of all squarefree numbers with greatest prime factor prime(n).

1, 2, 9, 60, 504, 6336, 89856, 1645056, 33094656, 801239040, 24246190080, 777550233600, 29697402470400, 1250501433753600, 55083063155097600, 2649111037319577600, 143390180403000115200, 8619643674791667302400, 534710099148093259776000, 36412881178052121329664000

Offset: 0

Author

Gus Wiseman, Dec 04 2020

Keywords

• nonn

Examples

			The initial terms are:
   1 = 1,
   2 = 2,
   9 = 3 + 6,
  60 = 5 + 10 + 15 + 30.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..349

Crossrefs

A010036 takes prime indices here to binary indices, row sums of A209862.

A048672 takes prime indices to binary indices in squarefree numbers.

A054640 divides the n-th term by prime(n), row sums of A261144.

A072047 counts prime factors of squarefree numbers.

A339194 is the restriction to semiprimes, row sums of A339116.

A339195 has this as row sums.

A002110 lists primorials.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes.

A056239 is the sum of prime indices of n (Heinz weight).

A246867 groups squarefree numbers by weight, with row sums A147655.

A319246 is the sum of prime indices of the n-th squarefree number.

A319247 lists reversed prime indices of squarefree numbers.

A329631 lists prime indices of squarefree numbers.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes.

Cf. A001221, A014466, A098350, A168472, A282935, A302590, A326878, A338901.

Programs

Maple

f:= proc(n) local i;
  `if`(n=0, 1, ithprime(n)) *mul(1+ithprime(i),i=1..n-1)
end proc:
map(f, [$0..20]); # Robert Israel, Dec 08 2020

Mathematica

Table[Sum[Times@@Prime/@stn,{stn,Select[Subsets[Range[n]],MemberQ[#,n]&]}],{n,10}]

Formula

For n >= 1, a(n) = A054640(n-1) * prime(n).

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 08 2025